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The probability of the sum X = X1 + X2 +···+ X n of n independent Bernoulli random variables deviating from its mean μ = ∑ i p i can be bounded using the Chernoff bound (Chernoff, 1952): where s = (1 + δ)μ.
Mean-square error of any estimation procedure can be bounded below by the Cramer-Rao lower bound (CRLB) [23].
Note that in the linear case this assumption is equivalent to the fact that b 3 u (t ) can be bounded; i.e., we have to bound three applications of the operator b to the exact solution.
(3.24) We need only to bound the first term on the right-hand side, since the second one can be bounded by symmetry.
The idea that it can be bounded in by honest conservatives in a Cabinet or restrained by normal constitutional limits is, to put it mildly, unsupported by history.
The first term can be bounded as follows: (D.132).
Therefore, error probability can be bounded as (D.28).
Their product can be bounded in the following way: (B19).
The values of, can be bounded from above as (26).
Consequently, the conditional probability can be bounded as (40).
Finally, using (2.26), can be bounded as follows: (2.36).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com